Updated on 2024/12/26

写真a

 
MINE, Masahiro
 
Affiliation
Affiliated organization, Global Education Center
Job title
Assistant Professor(without tenure)
Degree
Doctor of Science ( 2021.03 Tokyo Institute of Technology )
Homepage URL
https://sites.google.com/view/masaminemath/home

Research Experience

  • 2023.09
    -
    Now

    Waseda University   Global Education Center   Assistant Professor

  • 2023.04
    -
    Now

    Meiji Gakuin University   Part-time Lecturer

  • 2021.04
    -
    2021.08

    Sophia University   Faculty of Science and Technology   JSPS Research Fellow (PD)

  • 2019.04
    -
    2021.03

    Tokyo Institute of Technology   School of Science   JSPS Research Fellow (DC2)

Education Background

  • 2018.04
    -
    2021.03

    Tokyo Institute of Technology   School of Science   Doctoral course  

  • 2016.04
    -
    2018.03

    Tokyo Institute of Technology   School of Science   Master's course  

  • 2012.04
    -
    2016.03

    Tokyo Institute of Technology   School of Science   Bachelor's course  

Professional Memberships

  • 2018.04
    -
    Now

    The Mathematical Society of Japan

Research Areas

  • Algebra   Analytic Number Theory

Research Interests

  • Analytic Number Theory

  • zeta-function

  • L-function

  • probabilistic value-distribution

  • M-function

  • universality theorem

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Papers

  • Large deviations for values of L-functions attached to cusp forms in the level aspect

    Masahiro Mine

    Journal of the Mathematical Society of Japan   75 ( 3 )  2023.07  [Refereed]  [International journal]

    DOI

    Scopus

  • The value-distribution of Artin L-functions associated with cubic fields in conductor aspect

    Masahiro Mine

    Mathematische Zeitschrift   304 ( 4 )  2023.07  [Refereed]  [International journal]

    DOI

    Scopus

  • Probability density functions attached to random Euler products for automorphic L-functions

    Masahiro Mine

    The Quarterly Journal of Mathematics   73 ( 2 ) 397 - 442  2022.06  [Refereed]  [International journal]

    　View Summary

    Abstract

    In this paper, we study the value distributions of L-functions of holomorphic primitive cusp forms in the level aspect. We associate such automorphic L-functions with probabilistic models called the random Euler products. First, we prove the existence of probability density functions attached to the random Euler products. Then various mean values of automorphic L-functions are expressed as integrals involving the density functions. Moreover, we estimate the discrepancies between the distributions of values of automorphic L-functions and those of the random Euler products.

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • The density function for the value-distribution of the Lerch zeta-function and its applications

    Masahiro Mine

    Michigan Mathematical Journal   69 ( 4 ) 849 - 889  2020.10  [Refereed]  [International journal]

    　View Summary

    The probabilistic study of the value-distributions of zeta-functions is one of the modern topics in analytic number theory. In this paper, we study a certain probability measure related to the value-distribution of the Lerch zeta-function. We prove that it has a density function, and we can explicitly construct it. Moreover, we prove an asymptotic formula for the number of zeros of the Lerch zeta-function on the right side of the critical line, whose main term is associated with the density function.

    DOI

  • On certain mean values of logarithmic derivatives of L-functions and the related density functions

    Masahiro Mine

    Functiones et Approximatio Commentarii Mathematici   61 ( 2 ) 179 - 199  2019.12  [Refereed]  [International journal]

    　View Summary

    We study some density functions'' related to the value-distributions of L-functions. The first example of such a density function was given by Bohr and Jessen in 1930s for the Riemann zeta-function. In this paper, we construct construct density functions for a wide class of L-functions. We prove that certain mean values of L-functions in this class are represented as integrals involving the related density functions.

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • On M-functions for the value-distributions of L-functions

    Masahiro Mine

    Lithuanian Mathematical Journal   59 ( 1 ) 96 - 110  2019.01  [Refereed]  [International journal]

    　View Summary

    Bohr and Jessen proved the existence of a certain limit value regarded as the probability that values of the Riemann zeta function belong to a given region in the complex plane. They also studied the density of the probability, which has been called the M-function since the studies of Ihara and Matsumoto. In this paper, we construct M-functions for the value-distributions of L-functions in a class containing many kinds of zeta and L-functions. Moreover, we improve the estimate on the rate of the convergence of the limit studied by Bohr and Jessen.

    DOI

    Scopus

    1
    Citation
    (Scopus)

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Presentations

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Research Projects

  • ランダムディリクレ級数を用いたゼータ関数・多重ゼータ関数の研究

    日本学術振興会  科学研究費助成事業

    Project Year :

    2024.04
    -
    2029.03
     

    峰 正博

  • Value-distribution theory of zeta and multiple zeta functions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2022.04
    -
    2027.03
     

  • Probabilistic models of zeta-functions and applications to number theory

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2023.03
    -
    2024.03
     

  • On the density functions related to the value-distributions of zeta-functions

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2019.04
    -
    2021.03
     

    Masahiro Mine

Misc

  • An upper bound for the number of smooth values of a polynomial and its applications

    Masahiro Mine

    preprint on arXiv    2024.10

    Internal/External technical report, pre-print, etc.  

    　View Summary

    We provide a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of linear polynomials with integer coefficients. As an application, we fix an error in the proof of a result of Cassels which was used to prove that the Hurwitz zeta-function with algebraic irrational parameter has infinitely many zeros on the domain of convergence. We also apply the main result to a problem on primitive divisors of quadratic polynomials.

  • New developments toward the Gonek Conjecture on the Hurwitz zeta-function

    Masahiro Mine

    preprint on arXiv    2023.05

    Internal/External technical report, pre-print, etc.  

    　View Summary

    In this paper, we prove a version of the universality theorem for the Hurwitz zeta-function in the case where the parameter is algebraic and irrational. Then we apply the result to show that many of such Hurwitz zeta-functions have infinitely many zeros in the right half of the critical strip.

  • A random variable related to the Hurwitz zeta-function with algebraic parameter

    Masahiro Mine

    preprint on arXiv    2022.10

    Internal/External technical report, pre-print, etc.  

    　View Summary

    In this paper, we introduce a certain random variable closely related to the value-distribution of the Hurwitz zeta-function with algebraic parameter. We prove a version of the limit theorem, where the limit measure is presented by the law of this random variable. Then we apply it to show that any complex number can be approximated by values of the Hurwitz zeta-function for arbitrary quadratic irrational parameters but with finite exceptions.

  • On the value-distribution of the logarithms of symmetric power L-functions in the level aspect

    Philippe Lebacque, Kohji Matsumoto, Masahiro Mine, Yumiko Umegaki

    preprint on arXiv    2022.09  [International coauthorship]

    Internal/External technical report, pre-print, etc.  

    　View Summary

    We consider the value distribution of logarithms of symmetric power L-functions associated with newforms of even weight and prime power level. In the symmetric square case, under certain plausible analytical conditions, we prove that certain averages of those values in the level aspect, involving continuous bounded or Riemann integrable test functions, can be written as integrals involving a density function (the "M-function") which is related with the Sato-Tate measure. Moreover, even in the case of general symmetric power L-functions, we show the same type of formula when for some special type of test functions. We see that a kind of parity phenomenon of the density function exists.

  • Riemann ゼータ関数の対数の反復積分に対する極値分布

    峰 正博

    京都大学数理解析研究所講究録   2222   149 - 157  2022.01

    Research paper, summary (national, other academic conference)  

  • On the value-distribution of iterated integrals of the logarithm of the Riemann zeta-function II: probabilistic aspects

    Kenta Endo, Shōta Inoue, Masahiro Mine

    preprint on arXiv    2021.05

    Internal/External technical report, pre-print, etc.  

    　View Summary

    In this paper, we discuss the value-distribution of the Riemann
    zeta-function. The authors give some results for the discrepancy estimate and
    large deviations in the limit theorem by Bohr and Jessen.

  • 保型 L 関数の族の値分布について

    峰 正博

    京都大学数理解析研究所講究録   2162   1 - 9  2020.07

    Research paper, summary (national, other academic conference)  

  • Hurwitz ゼータ関数の値分布とそれに関連する密度関数

    峰 正博

    京都大学数理解析研究所講究録   2131   62 - 70  2019.10

    Research paper, summary (national, other academic conference)  

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